We want to study how to write a rotation as a 2 x 2 matrix. [br]We will treat is as a "black box" with inputs and outputs below.[br][br]You can adjust the angle of the rotation. Once chosen, you can vary the input and see how the output changes.
Set the angle of rotation to 30 degrees.[br][br]Test how the "black box" changes the input vector [math]\binom{1}{0}[/math]. Move the input to be the vector [math]\binom{1}{0}[/math].[br][br]Write the output vector below. [br][br][br]Enter as two numbers vertically: Example [br][br]0.345[br]0.222
Set the angle of rotation to 30 degrees.[br][br]Test how the "black box" changes the input vector [math]\binom{0}{1}[/math]. Move the input to be the vector [math]\binom{0}{1}[/math].[br][br]Write the output vector below. [br][br]Enter as two numbers vertically: Example [br][br]0.455[br]0.622
Now put the two answers from above together. What will be the transformation which rotates by 30 degrees?[br][br]Write as a 2 x 2 matrix: [br]Example:[br][br]0.345 0.455[br]0.222 0.622